Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [43,7,Mod(42,43)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(43, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("43.42");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 43 \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 43.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(9.89232559565\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} + 1038 x^{18} + 455829 x^{16} + 110435384 x^{14} + 16133606976 x^{12} + 1458210485616 x^{10} + \cdots + 64\!\cdots\!40 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{15} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 42.19 | ||
Root | \(13.7504i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 43.42 |
Dual form | 43.7.b.b.42.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/43\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 13.7504i | 1.71881i | 0.511299 | + | 0.859403i | \(0.329165\pi\) | ||||
−0.511299 | + | 0.859403i | \(0.670835\pi\) | |||||||
\(3\) | 14.6903i | 0.544084i | 0.962285 | + | 0.272042i | \(0.0876990\pi\) | ||||
−0.962285 | + | 0.272042i | \(0.912301\pi\) | |||||||
\(4\) | −125.075 | −1.95429 | ||||||||
\(5\) | − | 125.525i | − | 1.00420i | −0.864810 | − | 0.502100i | \(-0.832561\pi\) | ||
0.864810 | − | 0.502100i | \(-0.167439\pi\) | |||||||
\(6\) | −201.998 | −0.935176 | ||||||||
\(7\) | − | 485.131i | − | 1.41437i | −0.707026 | − | 0.707187i | \(-0.749964\pi\) | ||
0.707026 | − | 0.707187i | \(-0.250036\pi\) | |||||||
\(8\) | − | 839.807i | − | 1.64025i | ||||||
\(9\) | 513.196 | 0.703972 | ||||||||
\(10\) | 1726.02 | 1.72602 | ||||||||
\(11\) | −2195.16 | −1.64925 | −0.824626 | − | 0.565678i | \(-0.808615\pi\) | ||||
−0.824626 | + | 0.565678i | \(0.808615\pi\) | |||||||
\(12\) | − | 1837.38i | − | 1.06330i | ||||||
\(13\) | −2487.29 | −1.13213 | −0.566066 | − | 0.824360i | \(-0.691535\pi\) | ||||
−0.566066 | + | 0.824360i | \(0.691535\pi\) | |||||||
\(14\) | 6670.76 | 2.43104 | ||||||||
\(15\) | 1844.00 | 0.546369 | ||||||||
\(16\) | 3542.93 | 0.864973 | ||||||||
\(17\) | −3215.24 | −0.654435 | −0.327218 | − | 0.944949i | \(-0.606111\pi\) | ||||
−0.327218 | + | 0.944949i | \(0.606111\pi\) | |||||||
\(18\) | 7056.67i | 1.20999i | ||||||||
\(19\) | − | 828.174i | − | 0.120743i | −0.998176 | − | 0.0603713i | \(-0.980772\pi\) | ||
0.998176 | − | 0.0603713i | \(-0.0192285\pi\) | |||||||
\(20\) | 15700.0i | 1.96250i | ||||||||
\(21\) | 7126.70 | 0.769539 | ||||||||
\(22\) | − | 30184.4i | − | 2.83475i | ||||||
\(23\) | 11950.0 | 0.982164 | 0.491082 | − | 0.871113i | \(-0.336602\pi\) | ||||
0.491082 | + | 0.871113i | \(0.336602\pi\) | |||||||
\(24\) | 12337.0 | 0.892433 | ||||||||
\(25\) | −131.499 | −0.00841593 | ||||||||
\(26\) | − | 34201.4i | − | 1.94591i | ||||||
\(27\) | 18248.2i | 0.927105i | ||||||||
\(28\) | 60677.6i | 2.76411i | ||||||||
\(29\) | − | 39650.8i | − | 1.62576i | −0.582428 | − | 0.812882i | \(-0.697897\pi\) | ||
0.582428 | − | 0.812882i | \(-0.302103\pi\) | |||||||
\(30\) | 25355.8i | 0.939103i | ||||||||
\(31\) | −41667.8 | −1.39867 | −0.699335 | − | 0.714794i | \(-0.746520\pi\) | ||||
−0.699335 | + | 0.714794i | \(0.746520\pi\) | |||||||
\(32\) | − | 5030.75i | − | 0.153526i | ||||||
\(33\) | − | 32247.4i | − | 0.897333i | ||||||
\(34\) | − | 44211.0i | − | 1.12485i | ||||||
\(35\) | −60896.0 | −1.42031 | ||||||||
\(36\) | −64187.9 | −1.37577 | ||||||||
\(37\) | 67988.4i | 1.34224i | 0.741350 | + | 0.671119i | \(0.234186\pi\) | ||||
−0.741350 | + | 0.671119i | \(0.765814\pi\) | |||||||
\(38\) | 11387.8 | 0.207533 | ||||||||
\(39\) | − | 36539.0i | − | 0.615975i | ||||||
\(40\) | −105417. | −1.64714 | ||||||||
\(41\) | 15649.2 | 0.227060 | 0.113530 | − | 0.993535i | \(-0.463784\pi\) | ||||
0.113530 | + | 0.993535i | \(0.463784\pi\) | |||||||
\(42\) | 97995.4i | 1.32269i | ||||||||
\(43\) | −67467.7 | − | 42065.1i | −0.848576 | − | 0.529074i | ||||
\(44\) | 274559. | 3.22313 | ||||||||
\(45\) | − | 64418.8i | − | 0.706928i | ||||||
\(46\) | 164318.i | 1.68815i | ||||||||
\(47\) | 97342.7 | 0.937583 | 0.468792 | − | 0.883309i | \(-0.344690\pi\) | ||||
0.468792 | + | 0.883309i | \(0.344690\pi\) | |||||||
\(48\) | 52046.6i | 0.470618i | ||||||||
\(49\) | −117703. | −1.00046 | ||||||||
\(50\) | − | 1808.17i | − | 0.0144654i | ||||||
\(51\) | − | 47232.8i | − | 0.356068i | ||||||
\(52\) | 311098. | 2.21252 | ||||||||
\(53\) | −74224.0 | −0.498559 | −0.249280 | − | 0.968432i | \(-0.580194\pi\) | ||||
−0.249280 | + | 0.968432i | \(0.580194\pi\) | |||||||
\(54\) | −250921. | −1.59351 | ||||||||
\(55\) | 275547.i | 1.65618i | ||||||||
\(56\) | −407416. | −2.31993 | ||||||||
\(57\) | 12166.1 | 0.0656942 | ||||||||
\(58\) | 545216. | 2.79437 | ||||||||
\(59\) | −159976. | −0.778933 | −0.389466 | − | 0.921041i | \(-0.627341\pi\) | ||||
−0.389466 | + | 0.921041i | \(0.627341\pi\) | |||||||
\(60\) | −230637. | −1.06777 | ||||||||
\(61\) | 45475.1i | 0.200347i | 0.994970 | + | 0.100174i | \(0.0319399\pi\) | ||||
−0.994970 | + | 0.100174i | \(0.968060\pi\) | |||||||
\(62\) | − | 572950.i | − | 2.40404i | ||||||
\(63\) | − | 248967.i | − | 0.995681i | ||||||
\(64\) | 295923. | 1.12886 | ||||||||
\(65\) | 312217.i | 1.13689i | ||||||||
\(66\) | 443417. | 1.54234 | ||||||||
\(67\) | 59219.5 | 0.196898 | 0.0984488 | − | 0.995142i | \(-0.468612\pi\) | ||||
0.0984488 | + | 0.995142i | \(0.468612\pi\) | |||||||
\(68\) | 402146. | 1.27896 | ||||||||
\(69\) | 175549.i | 0.534380i | ||||||||
\(70\) | − | 837347.i | − | 2.44124i | ||||||
\(71\) | − | 450995.i | − | 1.26008i | −0.776564 | − | 0.630039i | \(-0.783039\pi\) | ||
0.776564 | − | 0.630039i | \(-0.216961\pi\) | |||||||
\(72\) | − | 430985.i | − | 1.15469i | ||||||
\(73\) | − | 102717.i | − | 0.264042i | −0.991247 | − | 0.132021i | \(-0.957853\pi\) | ||
0.991247 | − | 0.132021i | \(-0.0421466\pi\) | |||||||
\(74\) | −934870. | −2.30705 | ||||||||
\(75\) | − | 1931.76i | − | 0.00457898i | ||||||
\(76\) | 103584.i | 0.235967i | ||||||||
\(77\) | 1.06494e6i | 2.33266i | ||||||||
\(78\) | 502428. | 1.05874 | ||||||||
\(79\) | 2661.35 | 0.00539784 | 0.00269892 | − | 0.999996i | \(-0.499141\pi\) | ||||
0.00269892 | + | 0.999996i | \(0.499141\pi\) | |||||||
\(80\) | − | 444726.i | − | 0.868605i | ||||||
\(81\) | 106049. | 0.199549 | ||||||||
\(82\) | 215183.i | 0.390271i | ||||||||
\(83\) | −657618. | −1.15011 | −0.575055 | − | 0.818114i | \(-0.695020\pi\) | ||||
−0.575055 | + | 0.818114i | \(0.695020\pi\) | |||||||
\(84\) | −891371. | −1.50391 | ||||||||
\(85\) | 403593.i | 0.657183i | ||||||||
\(86\) | 578414. | − | 927711.i | 0.909376 | − | 1.45854i | ||||
\(87\) | 582481. | 0.884553 | ||||||||
\(88\) | 1.84351e6i | 2.70518i | ||||||||
\(89\) | 680976.i | 0.965966i | 0.875630 | + | 0.482983i | \(0.160447\pi\) | ||||
−0.875630 | + | 0.482983i | \(0.839553\pi\) | |||||||
\(90\) | 885788. | 1.21507 | ||||||||
\(91\) | 1.20666e6i | 1.60126i | ||||||||
\(92\) | −1.49464e6 | −1.91944 | ||||||||
\(93\) | − | 612111.i | − | 0.760994i | ||||||
\(94\) | 1.33851e6i | 1.61152i | ||||||||
\(95\) | −103956. | −0.121250 | ||||||||
\(96\) | 73903.2 | 0.0835313 | ||||||||
\(97\) | 1.25659e6 | 1.37682 | 0.688410 | − | 0.725322i | \(-0.258309\pi\) | ||||
0.688410 | + | 0.725322i | \(0.258309\pi\) | |||||||
\(98\) | − | 1.61846e6i | − | 1.71959i | ||||||
\(99\) | −1.12654e6 | −1.16103 | ||||||||
\(100\) | 16447.2 | 0.0164472 | ||||||||
\(101\) | 667424. | 0.647796 | 0.323898 | − | 0.946092i | \(-0.395007\pi\) | ||||
0.323898 | + | 0.946092i | \(0.395007\pi\) | |||||||
\(102\) | 649472. | 0.612012 | ||||||||
\(103\) | 946502. | 0.866184 | 0.433092 | − | 0.901350i | \(-0.357423\pi\) | ||||
0.433092 | + | 0.901350i | \(0.357423\pi\) | |||||||
\(104\) | 2.08885e6i | 1.85698i | ||||||||
\(105\) | − | 894579.i | − | 0.772771i | ||||||
\(106\) | − | 1.02061e6i | − | 0.856927i | ||||||
\(107\) | −1.85782e6 | −1.51654 | −0.758269 | − | 0.651942i | \(-0.773954\pi\) | ||||
−0.758269 | + | 0.651942i | \(0.773954\pi\) | |||||||
\(108\) | − | 2.28239e6i | − | 1.81184i | ||||||
\(109\) | −933301. | −0.720680 | −0.360340 | − | 0.932821i | \(-0.617339\pi\) | ||||
−0.360340 | + | 0.932821i | \(0.617339\pi\) | |||||||
\(110\) | −3.78889e6 | −2.84665 | ||||||||
\(111\) | −998768. | −0.730290 | ||||||||
\(112\) | − | 1.71878e6i | − | 1.22340i | ||||||
\(113\) | − | 618344.i | − | 0.428543i | −0.976774 | − | 0.214272i | \(-0.931262\pi\) | ||
0.976774 | − | 0.214272i | \(-0.0687377\pi\) | |||||||
\(114\) | 167289.i | 0.112916i | ||||||||
\(115\) | − | 1.50002e6i | − | 0.986288i | ||||||
\(116\) | 4.95931e6i | 3.17722i | ||||||||
\(117\) | −1.27647e6 | −0.796989 | ||||||||
\(118\) | − | 2.19975e6i | − | 1.33883i | ||||||
\(119\) | 1.55981e6i | 0.925616i | ||||||||
\(120\) | − | 1.54860e6i | − | 0.896181i | ||||||
\(121\) | 3.04715e6 | 1.72003 | ||||||||
\(122\) | −625303. | −0.344358 | ||||||||
\(123\) | 229891.i | 0.123540i | ||||||||
\(124\) | 5.21159e6 | 2.73341 | ||||||||
\(125\) | − | 1.94482e6i | − | 0.995748i | ||||||
\(126\) | 3.42341e6 | 1.71138 | ||||||||
\(127\) | −1.93152e6 | −0.942951 | −0.471475 | − | 0.881879i | \(-0.656278\pi\) | ||||
−0.471475 | + | 0.881879i | \(0.656278\pi\) | |||||||
\(128\) | 3.74710e6i | 1.78676i | ||||||||
\(129\) | 617948. | − | 991119.i | 0.287861 | − | 0.461697i | ||||
\(130\) | −4.29313e6 | −1.95409 | ||||||||
\(131\) | − | 3.53636e6i | − | 1.57305i | −0.617560 | − | 0.786524i | \(-0.711879\pi\) | ||
0.617560 | − | 0.786524i | \(-0.288121\pi\) | |||||||
\(132\) | 4.03334e6i | 1.75365i | ||||||||
\(133\) | −401772. | −0.170775 | ||||||||
\(134\) | 814295.i | 0.338429i | ||||||||
\(135\) | 2.29060e6 | 0.930998 | ||||||||
\(136\) | 2.70018e6i | 1.07344i | ||||||||
\(137\) | − | 4.20321e6i | − | 1.63463i | −0.576191 | − | 0.817315i | \(-0.695461\pi\) | ||
0.576191 | − | 0.817315i | \(-0.304539\pi\) | |||||||
\(138\) | −2.41387e6 | −0.918496 | ||||||||
\(139\) | 818972. | 0.304947 | 0.152474 | − | 0.988308i | \(-0.451276\pi\) | ||||
0.152474 | + | 0.988308i | \(0.451276\pi\) | |||||||
\(140\) | 7.61655e6 | 2.77571 | ||||||||
\(141\) | 1.42999e6i | 0.510124i | ||||||||
\(142\) | 6.20139e6 | 2.16583 | ||||||||
\(143\) | 5.45999e6 | 1.86717 | ||||||||
\(144\) | 1.81822e6 | 0.608917 | ||||||||
\(145\) | −4.97716e6 | −1.63259 | ||||||||
\(146\) | 1.41240e6 | 0.453837 | ||||||||
\(147\) | − | 1.72908e6i | − | 0.544332i | ||||||
\(148\) | − | 8.50363e6i | − | 2.62313i | ||||||
\(149\) | 2.95549e6i | 0.893452i | 0.894671 | + | 0.446726i | \(0.147410\pi\) | ||||
−0.894671 | + | 0.446726i | \(0.852590\pi\) | |||||||
\(150\) | 26562.5 | 0.00787038 | ||||||||
\(151\) | 6.37224e6i | 1.85081i | 0.378983 | + | 0.925404i | \(0.376274\pi\) | ||||
−0.378983 | + | 0.925404i | \(0.623726\pi\) | |||||||
\(152\) | −695506. | −0.198048 | ||||||||
\(153\) | −1.65005e6 | −0.460704 | ||||||||
\(154\) | −1.46434e7 | −4.00939 | ||||||||
\(155\) | 5.23034e6i | 1.40454i | ||||||||
\(156\) | 4.57011e6i | 1.20380i | ||||||||
\(157\) | − | 412869.i | − | 0.106687i | −0.998576 | − | 0.0533437i | \(-0.983012\pi\) | ||
0.998576 | − | 0.0533437i | \(-0.0169879\pi\) | |||||||
\(158\) | 36594.7i | 0.00927784i | ||||||||
\(159\) | − | 1.09037e6i | − | 0.271258i | ||||||
\(160\) | −631485. | −0.154171 | ||||||||
\(161\) | − | 5.79730e6i | − | 1.38915i | ||||||
\(162\) | 1.45822e6i | 0.342986i | ||||||||
\(163\) | − | 3.12906e6i | − | 0.722522i | −0.932465 | − | 0.361261i | \(-0.882346\pi\) | ||
0.932465 | − | 0.361261i | \(-0.117654\pi\) | |||||||
\(164\) | −1.95732e6 | −0.443741 | ||||||||
\(165\) | −4.04786e6 | −0.901101 | ||||||||
\(166\) | − | 9.04255e6i | − | 1.97682i | ||||||
\(167\) | −2.61032e6 | −0.560459 | −0.280229 | − | 0.959933i | \(-0.590411\pi\) | ||||
−0.280229 | + | 0.959933i | \(0.590411\pi\) | |||||||
\(168\) | − | 5.98505e6i | − | 1.26223i | ||||||
\(169\) | 1.35981e6 | 0.281721 | ||||||||
\(170\) | −5.54958e6 | −1.12957 | ||||||||
\(171\) | − | 425015.i | − | 0.0849995i | ||||||
\(172\) | 8.43851e6 | + | 5.26129e6i | 1.65837 | + | 1.03397i | ||||
\(173\) | 1.00269e7 | 1.93654 | 0.968270 | − | 0.249906i | \(-0.0803996\pi\) | ||||
0.968270 | + | 0.249906i | \(0.0803996\pi\) | |||||||
\(174\) | 8.00937e6i | 1.52038i | ||||||||
\(175\) | 63794.2i | 0.0119033i | ||||||||
\(176\) | −7.77728e6 | −1.42656 | ||||||||
\(177\) | − | 2.35010e6i | − | 0.423805i | ||||||
\(178\) | −9.36373e6 | −1.66031 | ||||||||
\(179\) | − | 3.42463e6i | − | 0.597111i | −0.954392 | − | 0.298555i | \(-0.903495\pi\) | ||
0.954392 | − | 0.298555i | \(-0.0965047\pi\) | |||||||
\(180\) | 8.05718e6i | 1.38155i | ||||||||
\(181\) | 6.31210e6 | 1.06448 | 0.532241 | − | 0.846593i | \(-0.321350\pi\) | ||||
0.532241 | + | 0.846593i | \(0.321350\pi\) | |||||||
\(182\) | −1.65921e7 | −2.75225 | ||||||||
\(183\) | −668041. | −0.109006 | ||||||||
\(184\) | − | 1.00357e7i | − | 1.61099i | ||||||
\(185\) | 8.53423e6 | 1.34787 | ||||||||
\(186\) | 8.41680e6 | 1.30800 | ||||||||
\(187\) | 7.05795e6 | 1.07933 | ||||||||
\(188\) | −1.21751e7 | −1.83231 | ||||||||
\(189\) | 8.85276e6 | 1.31127 | ||||||||
\(190\) | − | 1.42945e6i | − | 0.208405i | ||||||
\(191\) | 8.30483e6i | 1.19187i | 0.803031 | + | 0.595937i | \(0.203219\pi\) | ||||
−0.803031 | + | 0.595937i | \(0.796781\pi\) | |||||||
\(192\) | 4.34719e6i | 0.614193i | ||||||||
\(193\) | −4.83096e6 | −0.671988 | −0.335994 | − | 0.941864i | \(-0.609072\pi\) | ||||
−0.335994 | + | 0.941864i | \(0.609072\pi\) | |||||||
\(194\) | 1.72786e7i | 2.36649i | ||||||||
\(195\) | −4.58656e6 | −0.618562 | ||||||||
\(196\) | 1.47216e7 | 1.95519 | ||||||||
\(197\) | −6.48202e6 | −0.847835 | −0.423918 | − | 0.905701i | \(-0.639345\pi\) | ||||
−0.423918 | + | 0.905701i | \(0.639345\pi\) | |||||||
\(198\) | − | 1.54905e7i | − | 1.99558i | ||||||
\(199\) | 1.80084e6i | 0.228515i | 0.993451 | + | 0.114258i | \(0.0364490\pi\) | ||||
−0.993451 | + | 0.114258i | \(0.963551\pi\) | |||||||
\(200\) | 110434.i | 0.0138042i | ||||||||
\(201\) | 869951.i | 0.107129i | ||||||||
\(202\) | 9.17739e6i | 1.11343i | ||||||||
\(203\) | −1.92358e7 | −2.29944 | ||||||||
\(204\) | 5.90763e6i | 0.695862i | ||||||||
\(205\) | − | 1.96436e6i | − | 0.228013i | ||||||
\(206\) | 1.30148e7i | 1.48880i | ||||||||
\(207\) | 6.13268e6 | 0.691416 | ||||||||
\(208\) | −8.81230e6 | −0.979263 | ||||||||
\(209\) | 1.81797e6i | 0.199135i | ||||||||
\(210\) | 1.23009e7 | 1.32824 | ||||||||
\(211\) | 9.42048e6i | 1.00283i | 0.865208 | + | 0.501413i | \(0.167186\pi\) | ||||
−0.865208 | + | 0.501413i | \(0.832814\pi\) | |||||||
\(212\) | 9.28356e6 | 0.974332 | ||||||||
\(213\) | 6.62525e6 | 0.685588 | ||||||||
\(214\) | − | 2.55459e7i | − | 2.60663i | ||||||
\(215\) | −5.28022e6 | + | 8.46888e6i | −0.531296 | + | 0.852139i | ||||
\(216\) | 1.53250e7 | 1.52068 | ||||||||
\(217\) | 2.02143e7i | 1.97824i | ||||||||
\(218\) | − | 1.28333e7i | − | 1.23871i | ||||||
\(219\) | 1.50894e6 | 0.143661 | ||||||||
\(220\) | − | 3.44640e7i | − | 3.23666i | ||||||
\(221\) | 7.99724e6 | 0.740906 | ||||||||
\(222\) | − | 1.37335e7i | − | 1.25523i | ||||||
\(223\) | 5.46983e6i | 0.493241i | 0.969112 | + | 0.246620i | \(0.0793201\pi\) | ||||
−0.969112 | + | 0.246620i | \(0.920680\pi\) | |||||||
\(224\) | −2.44057e6 | −0.217144 | ||||||||
\(225\) | −67484.7 | −0.00592458 | ||||||||
\(226\) | 8.50250e6 | 0.736583 | ||||||||
\(227\) | − | 2.03320e7i | − | 1.73821i | −0.494627 | − | 0.869106i | \(-0.664695\pi\) | ||
0.494627 | − | 0.869106i | \(-0.335305\pi\) | |||||||
\(228\) | −1.52167e6 | −0.128386 | ||||||||
\(229\) | 1.81978e7 | 1.51535 | 0.757676 | − | 0.652631i | \(-0.226335\pi\) | ||||
0.757676 | + | 0.652631i | \(0.226335\pi\) | |||||||
\(230\) | 2.06260e7 | 1.69524 | ||||||||
\(231\) | −1.56442e7 | −1.26916 | ||||||||
\(232\) | −3.32990e7 | −2.66666 | ||||||||
\(233\) | − | 2.02178e7i | − | 1.59833i | −0.601111 | − | 0.799166i | \(-0.705275\pi\) | ||
0.601111 | − | 0.799166i | \(-0.294725\pi\) | |||||||
\(234\) | − | 1.75520e7i | − | 1.36987i | ||||||
\(235\) | − | 1.22189e7i | − | 0.941520i | ||||||
\(236\) | 2.00090e7 | 1.52226 | ||||||||
\(237\) | 39095.9i | 0.00293688i | ||||||||
\(238\) | −2.14481e7 | −1.59096 | ||||||||
\(239\) | −6.37752e6 | −0.467152 | −0.233576 | − | 0.972339i | \(-0.575043\pi\) | ||||
−0.233576 | + | 0.972339i | \(0.575043\pi\) | |||||||
\(240\) | 6.53315e6 | 0.472595 | ||||||||
\(241\) | − | 6.37244e6i | − | 0.455255i | −0.973748 | − | 0.227627i | \(-0.926903\pi\) | ||
0.973748 | − | 0.227627i | \(-0.0730968\pi\) | |||||||
\(242\) | 4.18996e7i | 2.95641i | ||||||||
\(243\) | 1.48608e7i | 1.03568i | ||||||||
\(244\) | − | 5.68779e6i | − | 0.391538i | ||||||
\(245\) | 1.47746e7i | 1.00466i | ||||||||
\(246\) | −3.16110e6 | −0.212341 | ||||||||
\(247\) | 2.05991e6i | 0.136697i | ||||||||
\(248\) | 3.49929e7i | 2.29416i | ||||||||
\(249\) | − | 9.66060e6i | − | 0.625757i | ||||||
\(250\) | 2.67422e7 | 1.71150 | ||||||||
\(251\) | −2.68750e7 | −1.69952 | −0.849761 | − | 0.527168i | \(-0.823254\pi\) | ||||
−0.849761 | + | 0.527168i | \(0.823254\pi\) | |||||||
\(252\) | 3.11395e7i | 1.94585i | ||||||||
\(253\) | −2.62321e7 | −1.61984 | ||||||||
\(254\) | − | 2.65593e7i | − | 1.62075i | ||||||
\(255\) | −5.92889e6 | −0.357563 | ||||||||
\(256\) | −3.25853e7 | −1.94223 | ||||||||
\(257\) | 6.95161e6i | 0.409530i | 0.978811 | + | 0.204765i | \(0.0656431\pi\) | ||||
−0.978811 | + | 0.204765i | \(0.934357\pi\) | |||||||
\(258\) | 1.36283e7 | + | 8.49706e6i | 0.793567 | + | 0.494777i | ||||
\(259\) | 3.29832e7 | 1.89843 | ||||||||
\(260\) | − | 3.90505e7i | − | 2.22181i | ||||||
\(261\) | − | 2.03486e7i | − | 1.14449i | ||||||
\(262\) | 4.86265e7 | 2.70376 | ||||||||
\(263\) | − | 5.84259e6i | − | 0.321172i | −0.987022 | − | 0.160586i | \(-0.948662\pi\) | ||
0.987022 | − | 0.160586i | \(-0.0513385\pi\) | |||||||
\(264\) | −2.70816e7 | −1.47185 | ||||||||
\(265\) | 9.31696e6i | 0.500653i | ||||||||
\(266\) | − | 5.52455e6i | − | 0.293530i | ||||||
\(267\) | −1.00037e7 | −0.525567 | ||||||||
\(268\) | −7.40687e6 | −0.384796 | ||||||||
\(269\) | 3.15131e6 | 0.161895 | 0.0809476 | − | 0.996718i | \(-0.474205\pi\) | ||||
0.0809476 | + | 0.996718i | \(0.474205\pi\) | |||||||
\(270\) | 3.14968e7i | 1.60020i | ||||||||
\(271\) | −1.99695e7 | −1.00337 | −0.501683 | − | 0.865051i | \(-0.667286\pi\) | ||||
−0.501683 | + | 0.865051i | \(0.667286\pi\) | |||||||
\(272\) | −1.13914e7 | −0.566069 | ||||||||
\(273\) | −1.77262e7 | −0.871219 | ||||||||
\(274\) | 5.77961e7 | 2.80961 | ||||||||
\(275\) | 288661. | 0.0138800 | ||||||||
\(276\) | − | 2.19567e7i | − | 1.04434i | ||||||
\(277\) | − | 2.84620e7i | − | 1.33914i | −0.742749 | − | 0.669570i | \(-0.766479\pi\) | ||
0.742749 | − | 0.669570i | \(-0.233521\pi\) | |||||||
\(278\) | 1.12612e7i | 0.524145i | ||||||||
\(279\) | −2.13837e7 | −0.984624 | ||||||||
\(280\) | 5.11408e7i | 2.32967i | ||||||||
\(281\) | 9.53964e6 | 0.429945 | 0.214973 | − | 0.976620i | \(-0.431034\pi\) | ||||
0.214973 | + | 0.976620i | \(0.431034\pi\) | |||||||
\(282\) | −1.96630e7 | −0.876805 | ||||||||
\(283\) | 1.28327e7 | 0.566186 | 0.283093 | − | 0.959092i | \(-0.408639\pi\) | ||||
0.283093 | + | 0.959092i | \(0.408639\pi\) | |||||||
\(284\) | 5.64082e7i | 2.46256i | ||||||||
\(285\) | − | 1.52715e6i | − | 0.0659700i | ||||||
\(286\) | 7.50774e7i | 3.20930i | ||||||||
\(287\) | − | 7.59189e6i | − | 0.321147i | ||||||
\(288\) | − | 2.58176e6i | − | 0.108078i | ||||||
\(289\) | −1.37998e7 | −0.571715 | ||||||||
\(290\) | − | 6.84382e7i | − | 2.80611i | ||||||
\(291\) | 1.84596e7i | 0.749106i | ||||||||
\(292\) | 1.28473e7i | 0.516016i | ||||||||
\(293\) | 4.00537e7 | 1.59235 | 0.796177 | − | 0.605063i | \(-0.206852\pi\) | ||||
0.796177 | + | 0.605063i | \(0.206852\pi\) | |||||||
\(294\) | 2.37757e7 | 0.935602 | ||||||||
\(295\) | 2.00810e7i | 0.782204i | ||||||||
\(296\) | 5.70971e7 | 2.20160 | ||||||||
\(297\) | − | 4.00576e7i | − | 1.52903i | ||||||
\(298\) | −4.06394e7 | −1.53567 | ||||||||
\(299\) | −2.97231e7 | −1.11194 | ||||||||
\(300\) | 241614.i | 0.00894867i | ||||||||
\(301\) | −2.04071e7 | + | 3.27306e7i | −0.748309 | + | 1.20020i | ||||
\(302\) | −8.76212e7 | −3.18118 | ||||||||
\(303\) | 9.80465e6i | 0.352455i | ||||||||
\(304\) | − | 2.93416e6i | − | 0.104439i | ||||||
\(305\) | 5.70825e6 | 0.201189 | ||||||||
\(306\) | − | 2.26889e7i | − | 0.791861i | ||||||
\(307\) | 2.94541e7 | 1.01796 | 0.508980 | − | 0.860779i | \(-0.330023\pi\) | ||||
0.508980 | + | 0.860779i | \(0.330023\pi\) | |||||||
\(308\) | − | 1.33197e8i | − | 4.55871i | ||||||
\(309\) | 1.39044e7i | 0.471277i | ||||||||
\(310\) | −7.19195e7 | −2.41414 | ||||||||
\(311\) | 2.31664e7 | 0.770154 | 0.385077 | − | 0.922884i | \(-0.374175\pi\) | ||||
0.385077 | + | 0.922884i | \(0.374175\pi\) | |||||||
\(312\) | −3.06857e7 | −1.01035 | ||||||||
\(313\) | − | 1.96712e7i | − | 0.641501i | −0.947164 | − | 0.320751i | \(-0.896065\pi\) | ||
0.947164 | − | 0.320751i | \(-0.103935\pi\) | |||||||
\(314\) | 5.67713e6 | 0.183375 | ||||||||
\(315\) | −3.12515e7 | −0.999862 | ||||||||
\(316\) | −332868. | −0.0105490 | ||||||||
\(317\) | −1.88268e7 | −0.591014 | −0.295507 | − | 0.955341i | \(-0.595489\pi\) | ||||
−0.295507 | + | 0.955341i | \(0.595489\pi\) | |||||||
\(318\) | 1.49931e7 | 0.466241 | ||||||||
\(319\) | 8.70396e7i | 2.68130i | ||||||||
\(320\) | − | 3.71457e7i | − | 1.13360i | ||||||
\(321\) | − | 2.72919e7i | − | 0.825124i | ||||||
\(322\) | 7.97155e7 | 2.38768 | ||||||||
\(323\) | 2.66278e6i | 0.0790182i | ||||||||
\(324\) | −1.32640e7 | −0.389978 | ||||||||
\(325\) | 327076. | 0.00952794 | ||||||||
\(326\) | 4.30260e7 | 1.24188 | ||||||||
\(327\) | − | 1.37105e7i | − | 0.392111i | ||||||
\(328\) | − | 1.31423e7i | − | 0.372434i | ||||||
\(329\) | − | 4.72239e7i | − | 1.32609i | ||||||
\(330\) | − | 5.56599e7i | − | 1.54882i | ||||||
\(331\) | 2.14243e7i | 0.590777i | 0.955377 | + | 0.295388i | \(0.0954490\pi\) | ||||
−0.955377 | + | 0.295388i | \(0.904551\pi\) | |||||||
\(332\) | 8.22515e7 | 2.24766 | ||||||||
\(333\) | 3.48913e7i | 0.944898i | ||||||||
\(334\) | − | 3.58930e7i | − | 0.963320i | ||||||
\(335\) | − | 7.43352e6i | − | 0.197724i | ||||||
\(336\) | 2.52494e7 | 0.665631 | ||||||||
\(337\) | 8.03689e6 | 0.209990 | 0.104995 | − | 0.994473i | \(-0.466517\pi\) | ||||
0.104995 | + | 0.994473i | \(0.466517\pi\) | |||||||
\(338\) | 1.86981e7i | 0.484224i | ||||||||
\(339\) | 9.08364e6 | 0.233164 | ||||||||
\(340\) | − | 5.04793e7i | − | 1.28433i | ||||||
\(341\) | 9.14672e7 | 2.30676 | ||||||||
\(342\) | 5.84415e6 | 0.146098 | ||||||||
\(343\) | 26029.3i | 0.000645029i | ||||||||
\(344\) | −3.53266e7 | + | 5.66598e7i | −0.867813 | + | 1.39187i | ||||
\(345\) | 2.20357e7 | 0.536624 | ||||||||
\(346\) | 1.37874e8i | 3.32854i | ||||||||
\(347\) | 8.81380e6i | 0.210948i | 0.994422 | + | 0.105474i | \(0.0336359\pi\) | ||||
−0.994422 | + | 0.105474i | \(0.966364\pi\) | |||||||
\(348\) | −7.28537e7 | −1.72868 | ||||||||
\(349\) | 3.08592e7i | 0.725953i | 0.931798 | + | 0.362976i | \(0.118239\pi\) | ||||
−0.931798 | + | 0.362976i | \(0.881761\pi\) | |||||||
\(350\) | −877198. | −0.0204594 | ||||||||
\(351\) | − | 4.53886e7i | − | 1.04960i | ||||||
\(352\) | 1.10433e7i | 0.253204i | ||||||||
\(353\) | 1.32889e7 | 0.302111 | 0.151055 | − | 0.988525i | \(-0.451733\pi\) | ||||
0.151055 | + | 0.988525i | \(0.451733\pi\) | |||||||
\(354\) | 3.23149e7 | 0.728439 | ||||||||
\(355\) | −5.66112e7 | −1.26537 | ||||||||
\(356\) | − | 8.51730e7i | − | 1.88778i | ||||||
\(357\) | −2.29141e7 | −0.503613 | ||||||||
\(358\) | 4.70902e7 | 1.02632 | ||||||||
\(359\) | −1.94769e7 | −0.420956 | −0.210478 | − | 0.977599i | \(-0.567502\pi\) | ||||
−0.210478 | + | 0.977599i | \(0.567502\pi\) | |||||||
\(360\) | −5.40994e7 | −1.15954 | ||||||||
\(361\) | 4.63600e7 | 0.985421 | ||||||||
\(362\) | 8.67943e7i | 1.82964i | ||||||||
\(363\) | 4.47634e7i | 0.935844i | ||||||||
\(364\) | − | 1.50923e8i | − | 3.12933i | ||||||
\(365\) | −1.28935e7 | −0.265151 | ||||||||
\(366\) | − | 9.18587e6i | − | 0.187360i | ||||||
\(367\) | 6.75278e7 | 1.36611 | 0.683053 | − | 0.730369i | \(-0.260652\pi\) | ||||
0.683053 | + | 0.730369i | \(0.260652\pi\) | |||||||
\(368\) | 4.23380e7 | 0.849545 | ||||||||
\(369\) | 8.03109e6 | 0.159844 | ||||||||
\(370\) | 1.17350e8i | 2.31673i | ||||||||
\(371\) | 3.60083e7i | 0.705150i | ||||||||
\(372\) | 7.65597e7i | 1.48721i | ||||||||
\(373\) | − | 8.90560e7i | − | 1.71608i | −0.513585 | − | 0.858039i | \(-0.671683\pi\) | ||
0.513585 | − | 0.858039i | \(-0.328317\pi\) | |||||||
\(374\) | 9.70500e7i | 1.85516i | ||||||||
\(375\) | 2.85699e7 | 0.541771 | ||||||||
\(376\) | − | 8.17491e7i | − | 1.53787i | ||||||
\(377\) | 9.86231e7i | 1.84058i | ||||||||
\(378\) | 1.21729e8i | 2.25382i | ||||||||
\(379\) | −1.05536e8 | −1.93857 | −0.969284 | − | 0.245942i | \(-0.920903\pi\) | ||||
−0.969284 | + | 0.245942i | \(0.920903\pi\) | |||||||
\(380\) | 1.30023e7 | 0.236958 | ||||||||
\(381\) | − | 2.83746e7i | − | 0.513045i | ||||||
\(382\) | −1.14195e8 | −2.04860 | ||||||||
\(383\) | − | 1.03036e8i | − | 1.83397i | −0.398920 | − | 0.916986i | \(-0.630615\pi\) | ||
0.398920 | − | 0.916986i | \(-0.369385\pi\) | |||||||
\(384\) | −5.50460e7 | −0.972147 | ||||||||
\(385\) | 1.33676e8 | 2.34246 | ||||||||
\(386\) | − | 6.64279e7i | − | 1.15502i | ||||||
\(387\) | −3.46241e7 | − | 2.15876e7i | −0.597374 | − | 0.372454i | ||||
\(388\) | −1.57167e8 | −2.69071 | ||||||||
\(389\) | − | 1.57030e7i | − | 0.266768i | −0.991064 | − | 0.133384i | \(-0.957416\pi\) | ||
0.991064 | − | 0.133384i | \(-0.0425843\pi\) | |||||||
\(390\) | − | 6.30672e7i | − | 1.06319i | ||||||
\(391\) | −3.84221e7 | −0.642762 | ||||||||
\(392\) | 9.88475e7i | 1.64100i | ||||||||
\(393\) | 5.19500e7 | 0.855871 | ||||||||
\(394\) | − | 8.91306e7i | − | 1.45726i | ||||||
\(395\) | − | 334065.i | − | 0.00542051i | ||||||
\(396\) | 1.40902e8 | 2.26899 | ||||||||
\(397\) | −7.90324e7 | −1.26309 | −0.631544 | − | 0.775340i | \(-0.717578\pi\) | ||||
−0.631544 | + | 0.775340i | \(0.717578\pi\) | |||||||
\(398\) | −2.47623e7 | −0.392774 | ||||||||
\(399\) | − | 5.90215e6i | − | 0.0929162i | ||||||
\(400\) | −465892. | −0.00727956 | ||||||||
\(401\) | −4.44435e7 | −0.689247 | −0.344623 | − | 0.938741i | \(-0.611993\pi\) | ||||
−0.344623 | + | 0.938741i | \(0.611993\pi\) | |||||||
\(402\) | −1.19622e7 | −0.184134 | ||||||||
\(403\) | 1.03640e8 | 1.58348 | ||||||||
\(404\) | −8.34780e7 | −1.26598 | ||||||||
\(405\) | − | 1.33117e7i | − | 0.200387i | ||||||
\(406\) | − | 2.64501e8i | − | 3.95229i | ||||||
\(407\) | − | 1.49245e8i | − | 2.21369i | ||||||
\(408\) | −3.96664e7 | −0.584039 | ||||||||
\(409\) | 7.23937e7i | 1.05811i | 0.848587 | + | 0.529055i | \(0.177454\pi\) | ||||
−0.848587 | + | 0.529055i | \(0.822546\pi\) | |||||||
\(410\) | 2.70108e7 | 0.391910 | ||||||||
\(411\) | 6.17464e7 | 0.889377 | ||||||||
\(412\) | −1.18384e8 | −1.69278 | ||||||||
\(413\) | 7.76095e7i | 1.10170i | ||||||||
\(414\) | 8.43271e7i | 1.18841i | ||||||||
\(415\) | 8.25475e7i | 1.15494i | ||||||||
\(416\) | 1.25130e7i | 0.173812i | ||||||||
\(417\) | 1.20309e7i | 0.165917i | ||||||||
\(418\) | −2.49979e7 | −0.342275 | ||||||||
\(419\) | − | 2.13499e7i | − | 0.290238i | −0.989414 | − | 0.145119i | \(-0.953644\pi\) | ||
0.989414 | − | 0.145119i | \(-0.0463564\pi\) | |||||||
\(420\) | 1.11889e8i | 1.51022i | ||||||||
\(421\) | − | 7.59636e7i | − | 1.01803i | −0.860758 | − | 0.509014i | \(-0.830010\pi\) | ||
0.860758 | − | 0.509014i | \(-0.169990\pi\) | |||||||
\(422\) | −1.29536e8 | −1.72366 | ||||||||
\(423\) | 4.99558e7 | 0.660032 | ||||||||
\(424\) | 6.23338e7i | 0.817761i | ||||||||
\(425\) | 422801. | 0.00550768 | ||||||||
\(426\) | 9.11002e7i | 1.17839i | ||||||||
\(427\) | 2.20613e7 | 0.283366 | ||||||||
\(428\) | 2.32367e8 | 2.96376 | ||||||||
\(429\) | 8.02088e7i | 1.01590i | ||||||||
\(430\) | −1.16451e8 | − | 7.26054e7i | −1.46466 | − | 0.913195i | ||||
\(431\) | −2.01234e7 | −0.251344 | −0.125672 | − | 0.992072i | \(-0.540109\pi\) | ||||
−0.125672 | + | 0.992072i | \(0.540109\pi\) | |||||||
\(432\) | 6.46521e7i | 0.801921i | ||||||||
\(433\) | 2.28719e7i | 0.281733i | 0.990029 | + | 0.140866i | \(0.0449888\pi\) | ||||
−0.990029 | + | 0.140866i | \(0.955011\pi\) | |||||||
\(434\) | −2.77956e8 | −3.40022 | ||||||||
\(435\) | − | 7.31158e7i | − | 0.888267i | ||||||
\(436\) | 1.16733e8 | 1.40842 | ||||||||
\(437\) | − | 9.89667e6i | − | 0.118589i | ||||||
\(438\) | 2.07486e7i | 0.246926i | ||||||||
\(439\) | −1.12643e8 | −1.33141 | −0.665705 | − | 0.746215i | \(-0.731869\pi\) | ||||
−0.665705 | + | 0.746215i | \(0.731869\pi\) | |||||||
\(440\) | 2.31406e8 | 2.71654 | ||||||||
\(441\) | −6.04045e7 | −0.704293 | ||||||||
\(442\) | 1.09966e8i | 1.27347i | ||||||||
\(443\) | −1.00154e8 | −1.15201 | −0.576007 | − | 0.817445i | \(-0.695390\pi\) | ||||
−0.576007 | + | 0.817445i | \(0.695390\pi\) | |||||||
\(444\) | 1.24921e8 | 1.42720 | ||||||||
\(445\) | 8.54794e7 | 0.970022 | ||||||||
\(446\) | −7.52126e7 | −0.847785 | ||||||||
\(447\) | −4.34170e7 | −0.486113 | ||||||||
\(448\) | − | 1.43561e8i | − | 1.59662i | ||||||
\(449\) | − | 2.24376e7i | − | 0.247878i | −0.992290 | − | 0.123939i | \(-0.960447\pi\) | ||
0.992290 | − | 0.123939i | \(-0.0395527\pi\) | |||||||
\(450\) | − | 927945.i | − | 0.0101832i | ||||||
\(451\) | −3.43524e7 | −0.374479 | ||||||||
\(452\) | 7.73392e7i | 0.837500i | ||||||||
\(453\) | −9.36100e7 | −1.00700 | ||||||||
\(454\) | 2.79574e8 | 2.98765 | ||||||||
\(455\) | 1.51466e8 | 1.60798 | ||||||||
\(456\) | − | 1.02172e7i | − | 0.107755i | ||||||
\(457\) | − | 2.72646e7i | − | 0.285660i | −0.989747 | − | 0.142830i | \(-0.954380\pi\) | ||
0.989747 | − | 0.142830i | \(-0.0456203\pi\) | |||||||
\(458\) | 2.50229e8i | 2.60460i | ||||||||
\(459\) | − | 5.86723e7i | − | 0.606730i | ||||||
\(460\) | 1.87615e8i | 1.92750i | ||||||||
\(461\) | 1.10894e8 | 1.13189 | 0.565945 | − | 0.824443i | \(-0.308511\pi\) | ||||
0.565945 | + | 0.824443i | \(0.308511\pi\) | |||||||
\(462\) | − | 2.15115e8i | − | 2.18145i | ||||||
\(463\) | − | 4.40459e6i | − | 0.0443775i | −0.999754 | − | 0.0221887i | \(-0.992937\pi\) | ||
0.999754 | − | 0.0221887i | \(-0.00706348\pi\) | |||||||
\(464\) | − | 1.40480e8i | − | 1.40624i | ||||||
\(465\) | −7.68352e7 | −0.764190 | ||||||||
\(466\) | 2.78004e8 | 2.74722 | ||||||||
\(467\) | 1.58915e7i | 0.156032i | 0.996952 | + | 0.0780160i | \(0.0248585\pi\) | ||||
−0.996952 | + | 0.0780160i | \(0.975141\pi\) | |||||||
\(468\) | 1.59654e8 | 1.55755 | ||||||||
\(469\) | − | 2.87292e7i | − | 0.278487i | ||||||
\(470\) | 1.68016e8 | 1.61829 | ||||||||
\(471\) | 6.06516e6 | 0.0580470 | ||||||||
\(472\) | 1.34349e8i | 1.27764i | ||||||||
\(473\) | 1.48102e8 | + | 9.23394e7i | 1.39952 | + | 0.872577i | ||||
\(474\) | −537586. | −0.00504793 | ||||||||
\(475\) | 108904.i | 0.00101616i | ||||||||
\(476\) | − | 1.95093e8i | − | 1.80893i | ||||||
\(477\) | −3.80915e7 | −0.350972 | ||||||||
\(478\) | − | 8.76938e7i | − | 0.802944i | ||||||
\(479\) | −5.66316e7 | −0.515290 | −0.257645 | − | 0.966240i | \(-0.582947\pi\) | ||||
−0.257645 | + | 0.966240i | \(0.582947\pi\) | |||||||
\(480\) | − | 9.27669e6i | − | 0.0838821i | ||||||
\(481\) | − | 1.69107e8i | − | 1.51959i | ||||||
\(482\) | 8.76239e7 | 0.782495 | ||||||||
\(483\) | 8.51640e7 | 0.755814 | ||||||||
\(484\) | −3.81121e8 | −3.36145 | ||||||||
\(485\) | − | 1.57733e8i | − | 1.38260i | ||||||
\(486\) | −2.04343e8 | −1.78013 | ||||||||
\(487\) | −8.26005e7 | −0.715147 | −0.357574 | − | 0.933885i | \(-0.616396\pi\) | ||||
−0.357574 | + | 0.933885i | \(0.616396\pi\) | |||||||
\(488\) | 3.81903e7 | 0.328619 | ||||||||
\(489\) | 4.59668e7 | 0.393113 | ||||||||
\(490\) | −2.03158e8 | −1.72681 | ||||||||
\(491\) | − | 1.04983e8i | − | 0.886898i | −0.896300 | − | 0.443449i | \(-0.853755\pi\) | ||
0.896300 | − | 0.443449i | \(-0.146245\pi\) | |||||||
\(492\) | − | 2.87535e7i | − | 0.241433i | ||||||
\(493\) | 1.27487e8i | 1.06396i | ||||||||
\(494\) | −2.83247e7 | −0.234955 | ||||||||
\(495\) | 1.41409e8i | 1.16590i | ||||||||
\(496\) | −1.47626e8 | −1.20981 | ||||||||
\(497\) | −2.18792e8 | −1.78222 | ||||||||
\(498\) | 1.32838e8 | 1.07556 | ||||||||
\(499\) | 9.42511e7i | 0.758551i | 0.925284 | + | 0.379275i | \(0.123827\pi\) | ||||
−0.925284 | + | 0.379275i | \(0.876173\pi\) | |||||||
\(500\) | 2.43248e8i | 1.94598i | ||||||||
\(501\) | − | 3.83463e7i | − | 0.304937i | ||||||
\(502\) | − | 3.69543e8i | − | 2.92115i | ||||||
\(503\) | − | 9.27104e6i | − | 0.0728492i | −0.999336 | − | 0.0364246i | \(-0.988403\pi\) | ||
0.999336 | − | 0.0364246i | \(-0.0115969\pi\) | |||||||
\(504\) | −2.09084e8 | −1.63316 | ||||||||
\(505\) | − | 8.37784e7i | − | 0.650516i | ||||||
\(506\) | − | 3.60703e8i | − | 2.78418i | ||||||
\(507\) | 1.99761e7i | 0.153280i | ||||||||
\(508\) | 2.41585e8 | 1.84280 | ||||||||
\(509\) | −2.93942e7 | −0.222899 | −0.111450 | − | 0.993770i | \(-0.535549\pi\) | ||||
−0.111450 | + | 0.993770i | \(0.535549\pi\) | |||||||
\(510\) | − | 8.15249e7i | − | 0.614582i | ||||||
\(511\) | −4.98311e7 | −0.373454 | ||||||||
\(512\) | − | 2.08248e8i | − | 1.55157i | ||||||
\(513\) | 1.51127e7 | 0.111941 | ||||||||
\(514\) | −9.55878e7 | −0.703903 | ||||||||
\(515\) | − | 1.18810e8i | − | 0.869821i | ||||||
\(516\) | −7.72898e7 | + | 1.23964e8i | −0.562565 | + | 0.902291i | ||||
\(517\) | −2.13682e8 | −1.54631 | ||||||||
\(518\) | 4.53534e8i | 3.26303i | ||||||||
\(519\) | 1.47297e8i | 1.05364i | ||||||||
\(520\) | 2.62202e8 | 1.86477 | ||||||||
\(521\) | − | 4.15492e7i | − | 0.293798i | −0.989151 | − | 0.146899i | \(-0.953071\pi\) | ||
0.989151 | − | 0.146899i | \(-0.0469293\pi\) | |||||||
\(522\) | 2.79802e8 | 1.96716 | ||||||||
\(523\) | 1.31954e8i | 0.922397i | 0.887297 | + | 0.461199i | \(0.152580\pi\) | ||||
−0.887297 | + | 0.461199i | \(0.847420\pi\) | |||||||
\(524\) | 4.42309e8i | 3.07420i | ||||||||
\(525\) | −937154. | −0.00647639 | ||||||||
\(526\) | 8.03382e7 | 0.552033 | ||||||||
\(527\) | 1.33972e8 | 0.915338 | ||||||||
\(528\) | − | 1.14250e8i | − | 0.776169i | ||||||
\(529\) | −5.23372e6 | −0.0353544 | ||||||||
\(530\) | −1.28112e8 | −0.860525 | ||||||||
\(531\) | −8.20992e7 | −0.548347 | ||||||||
\(532\) | 5.02516e7 | 0.333745 | ||||||||
\(533\) | −3.89241e7 | −0.257061 | ||||||||
\(534\) | − | 1.37556e8i | − | 0.903348i | ||||||
\(535\) | 2.33203e8i | 1.52291i | ||||||||
\(536\) | − | 4.97329e7i | − | 0.322961i | ||||||
\(537\) | 5.03088e7 | 0.324879 | ||||||||
\(538\) | 4.33319e7i | 0.278267i | ||||||||
\(539\) | 2.58376e8 | 1.65000 | ||||||||
\(540\) | −2.86497e8 | −1.81944 | ||||||||
\(541\) | −6.45179e7 | −0.407463 | −0.203732 | − | 0.979027i | \(-0.565307\pi\) | ||||
−0.203732 | + | 0.979027i | \(0.565307\pi\) | |||||||
\(542\) | − | 2.74590e8i | − | 1.72459i | ||||||
\(543\) | 9.27266e7i | 0.579168i | ||||||||
\(544\) | 1.61751e7i | 0.100473i | ||||||||
\(545\) | 1.17153e8i | 0.723706i | ||||||||
\(546\) | − | 2.43743e8i | − | 1.49746i | ||||||
\(547\) | 1.36234e8 | 0.832383 | 0.416192 | − | 0.909277i | \(-0.363365\pi\) | ||||
0.416192 | + | 0.909277i | \(0.363365\pi\) | |||||||
\(548\) | 5.25716e8i | 3.19455i | ||||||||
\(549\) | 2.33376e7i | 0.141039i | ||||||||
\(550\) | 3.96921e6i | 0.0238570i | ||||||||
\(551\) | −3.28377e7 | −0.196299 | ||||||||
\(552\) | 1.47427e8 | 0.876515 | ||||||||
\(553\) | − | 1.29110e6i | − | 0.00763457i | ||||||
\(554\) | 3.91365e8 | 2.30172 | ||||||||
\(555\) | 1.25370e8i | 0.733357i | ||||||||
\(556\) | −1.02433e8 | −0.595957 | ||||||||
\(557\) | −2.82425e8 | −1.63432 | −0.817162 | − | 0.576409i | \(-0.804454\pi\) | ||||
−0.817162 | + | 0.576409i | \(0.804454\pi\) | |||||||
\(558\) | − | 2.94036e8i | − | 1.69238i | ||||||
\(559\) | 1.67812e8 | + | 1.04628e8i | 0.960699 | + | 0.598982i | ||||
\(560\) | −2.15750e8 | −1.22853 | ||||||||
\(561\) | 1.03683e8i | 0.587246i | ||||||||
\(562\) | 1.31174e8i | 0.738992i | ||||||||
\(563\) | −5.27513e7 | −0.295602 | −0.147801 | − | 0.989017i | \(-0.547220\pi\) | ||||
−0.147801 | + | 0.989017i | \(0.547220\pi\) | |||||||
\(564\) | − | 1.78856e8i | − | 0.996933i | ||||||
\(565\) | −7.76175e7 | −0.430343 | ||||||||
\(566\) | 1.76456e8i | 0.973164i | ||||||||
\(567\) | − | 5.14474e7i | − | 0.282237i | ||||||
\(568\) | −3.78749e8 | −2.06684 | ||||||||
\(569\) | −4.29511e7 | −0.233151 | −0.116576 | − | 0.993182i | \(-0.537192\pi\) | ||||
−0.116576 | + | 0.993182i | \(0.537192\pi\) | |||||||
\(570\) | 2.09990e7 | 0.113390 | ||||||||
\(571\) | − | 2.78688e8i | − | 1.49696i | −0.663157 | − | 0.748481i | \(-0.730784\pi\) | ||
0.663157 | − | 0.748481i | \(-0.269216\pi\) | |||||||
\(572\) | −6.82908e8 | −3.64900 | ||||||||
\(573\) | −1.22000e8 | −0.648480 | ||||||||
\(574\) | 1.04392e8 | 0.551990 | ||||||||
\(575\) | −1.57141e6 | −0.00826582 | ||||||||
\(576\) | 1.51866e8 | 0.794683 | ||||||||
\(577\) | 8.60563e7i | 0.447976i | 0.974592 | + | 0.223988i | \(0.0719077\pi\) | ||||
−0.974592 | + | 0.223988i | \(0.928092\pi\) | |||||||
\(578\) | − | 1.89754e8i | − | 0.982667i | ||||||
\(579\) | − | 7.09682e7i | − | 0.365618i | ||||||
\(580\) | 6.22517e8 | 3.19056 | ||||||||
\(581\) | 3.19031e8i | 1.62669i | ||||||||
\(582\) | −2.53828e8 | −1.28757 | ||||||||
\(583\) | 1.62933e8 | 0.822250 | ||||||||
\(584\) | −8.62623e7 | −0.433094 | ||||||||
\(585\) | 1.60228e8i | 0.800336i | ||||||||
\(586\) | 5.50756e8i | 2.73695i | ||||||||
\(587\) | − | 2.26249e8i | − | 1.11859i | −0.828967 | − | 0.559297i | \(-0.811071\pi\) | ||
0.828967 | − | 0.559297i | \(-0.188929\pi\) | |||||||
\(588\) | 2.16265e8i | 1.06379i | ||||||||
\(589\) | 3.45081e7i | 0.168879i | ||||||||
\(590\) | −2.76123e8 | −1.34446 | ||||||||
\(591\) | − | 9.52226e7i | − | 0.461294i | ||||||
\(592\) | 2.40878e8i | 1.16100i | ||||||||
\(593\) | 1.03816e8i | 0.497852i | 0.968523 | + | 0.248926i | \(0.0800775\pi\) | ||||
−0.968523 | + | 0.248926i | \(0.919922\pi\) | |||||||
\(594\) | 5.50810e8 | 2.62811 | ||||||||
\(595\) | 1.95795e8 | 0.929503 | ||||||||
\(596\) | − | 3.69658e8i | − | 1.74607i | ||||||
\(597\) | −2.64548e7 | −0.124332 | ||||||||
\(598\) | − | 4.08706e8i | − | 1.91121i | ||||||
\(599\) | 1.57390e8 | 0.732313 | 0.366156 | − | 0.930553i | \(-0.380673\pi\) | ||||
0.366156 | + | 0.930553i | \(0.380673\pi\) | |||||||
\(600\) | −1.62230e6 | −0.00751066 | ||||||||
\(601\) | 7.90290e7i | 0.364052i | 0.983294 | + | 0.182026i | \(0.0582655\pi\) | ||||
−0.983294 | + | 0.182026i | \(0.941735\pi\) | |||||||
\(602\) | −4.50061e8 | − | 2.80606e8i | −2.06292 | − | 1.28620i | ||||
\(603\) | 3.03912e7 | 0.138610 | ||||||||
\(604\) | − | 7.97007e8i | − | 3.61702i | ||||||
\(605\) | − | 3.82493e8i | − | 1.72726i | ||||||
\(606\) | −1.34818e8 | −0.605803 | ||||||||
\(607\) | 1.34486e8i | 0.601326i | 0.953730 | + | 0.300663i | \(0.0972080\pi\) | ||||
−0.953730 | + | 0.300663i | \(0.902792\pi\) | |||||||
\(608\) | −4.16634e6 | −0.0185372 | ||||||||
\(609\) | − | 2.82579e8i | − | 1.25109i | ||||||
\(610\) | 7.84910e7i | 0.345804i | ||||||||
\(611\) | −2.42120e8 | −1.06147 | ||||||||
\(612\) | 2.06379e8 | 0.900352 | ||||||||
\(613\) | −2.33648e8 | −1.01433 | −0.507167 | − | 0.861848i | \(-0.669307\pi\) | ||||
−0.507167 | + | 0.861848i | \(0.669307\pi\) | |||||||
\(614\) | 4.05007e8i | 1.74967i | ||||||||
\(615\) | 2.88570e7 | 0.124058 | ||||||||
\(616\) | 8.94341e8 | 3.82614 | ||||||||
\(617\) | 3.91319e8 | 1.66600 | 0.833001 | − | 0.553272i | \(-0.186621\pi\) | ||||
0.833001 | + | 0.553272i | \(0.186621\pi\) | |||||||
\(618\) | −1.91191e8 | −0.810034 | ||||||||
\(619\) | −5.31148e7 | −0.223946 | −0.111973 | − | 0.993711i | \(-0.535717\pi\) | ||||
−0.111973 | + | 0.993711i | \(0.535717\pi\) | |||||||
\(620\) | − | 6.54184e8i | − | 2.74489i | ||||||
\(621\) | 2.18066e8i | 0.910569i | ||||||||
\(622\) | 3.18549e8i | 1.32375i | ||||||||
\(623\) | 3.30362e8 | 1.36624 | ||||||||
\(624\) | − | 1.29455e8i | − | 0.532802i | ||||||
\(625\) | −2.46178e8 | −1.00835 | ||||||||
\(626\) | 2.70488e8 | 1.10262 | ||||||||
\(627\) | −2.67065e7 | −0.108346 | ||||||||
\(628\) | 5.16395e7i | 0.208499i | ||||||||
\(629\) | − | 2.18599e8i | − | 0.878407i | ||||||
\(630\) | − | 4.29723e8i | − | 1.71857i | ||||||
\(631\) | − | 1.17430e7i | − | 0.0467403i | −0.999727 | − | 0.0233702i | \(-0.992560\pi\) | ||
0.999727 | − | 0.0233702i | \(-0.00743963\pi\) | |||||||
\(632\) | − | 2.23502e6i | − | 0.00885380i | ||||||
\(633\) | −1.38389e8 | −0.545622 | ||||||||
\(634\) | − | 2.58877e8i | − | 1.01584i | ||||||
\(635\) | 2.42454e8i | 0.946910i | ||||||||
\(636\) | 1.36378e8i | 0.530119i | ||||||||
\(637\) | 2.92761e8 | 1.13265 | ||||||||
\(638\) | −1.19683e9 | −4.60863 | ||||||||
\(639\) | − | 2.31449e8i | − | 0.887059i | ||||||
\(640\) | 4.70355e8 | 1.79426 | ||||||||
\(641\) | 2.37189e8i | 0.900575i | 0.892884 | + | 0.450287i | \(0.148678\pi\) | ||||
−0.892884 | + | 0.450287i | \(0.851322\pi\) | |||||||
\(642\) | 3.75277e8 | 1.41823 | ||||||||
\(643\) | −2.27808e8 | −0.856913 | −0.428456 | − | 0.903562i | \(-0.640942\pi\) | ||||
−0.428456 | + | 0.903562i | \(0.640942\pi\) | |||||||
\(644\) | 7.25097e8i | 2.71480i | ||||||||
\(645\) | −1.24410e8 | − | 7.75679e7i | −0.463635 | − | 0.289070i | ||||
\(646\) | −3.66144e7 | −0.135817 | ||||||||
\(647\) | − | 1.03798e8i | − | 0.383243i | −0.981469 | − | 0.191621i | \(-0.938625\pi\) | ||
0.981469 | − | 0.191621i | \(-0.0613746\pi\) | |||||||
\(648\) | − | 8.90603e7i | − | 0.327310i | ||||||
\(649\) | 3.51173e8 | 1.28466 | ||||||||
\(650\) | 4.49745e6i | 0.0163767i | ||||||||
\(651\) | −2.96954e8 | −1.07633 | ||||||||
\(652\) | 3.91367e8i | 1.41202i | ||||||||
\(653\) | 1.89194e8i | 0.679466i | 0.940522 | + | 0.339733i | \(0.110337\pi\) | ||||
−0.940522 | + | 0.339733i | \(0.889663\pi\) | |||||||
\(654\) | 1.88525e8 | 0.673962 | ||||||||
\(655\) | −4.43901e8 | −1.57965 | ||||||||
\(656\) | 5.54439e7 | 0.196400 | ||||||||
\(657\) | − | 5.27138e7i | − | 0.185878i | ||||||
\(658\) | 6.49350e8 | 2.27930 | ||||||||
\(659\) | 2.37555e8 | 0.830056 | 0.415028 | − | 0.909809i | \(-0.363772\pi\) | ||||
0.415028 | + | 0.909809i | \(0.363772\pi\) | |||||||
\(660\) | 5.06285e8 | 1.76102 | ||||||||
\(661\) | −2.01381e8 | −0.697292 | −0.348646 | − | 0.937254i | \(-0.613358\pi\) | ||||
−0.348646 | + | 0.937254i | \(0.613358\pi\) | |||||||
\(662\) | −2.94594e8 | −1.01543 | ||||||||
\(663\) | 1.17482e8i | 0.403116i | ||||||||
\(664\) | 5.52272e8i | 1.88647i | ||||||||
\(665\) | 5.04324e7i | 0.171492i | ||||||||
\(666\) | −4.79772e8 | −1.62410 | ||||||||
\(667\) | − | 4.73826e8i | − | 1.59677i | ||||||
\(668\) | 3.26485e8 | 1.09530 | ||||||||
\(669\) | −8.03533e7 | −0.268365 | ||||||||
\(670\) | 1.02214e8 | 0.339850 | ||||||||
\(671\) | − | 9.98248e7i | − | 0.330424i | ||||||
\(672\) | − | 3.58527e7i | − | 0.118145i | ||||||
\(673\) | − | 2.44156e8i | − | 0.800980i | −0.916301 | − | 0.400490i | \(-0.868840\pi\) | ||
0.916301 | − | 0.400490i | \(-0.131160\pi\) | |||||||
\(674\) | 1.10511e8i | 0.360932i | ||||||||
\(675\) | − | 2.39962e6i | − | 0.00780245i | ||||||
\(676\) | −1.70079e8 | −0.550566 | ||||||||
\(677\) | 1.87157e8i | 0.603170i | 0.953439 | + | 0.301585i | \(0.0975157\pi\) | ||||
−0.953439 | + | 0.301585i | \(0.902484\pi\) | |||||||
\(678\) | 1.24904e8i | 0.400763i | ||||||||
\(679\) | − | 6.09608e8i | − | 1.94734i | ||||||
\(680\) | 3.38940e8 | 1.07794 | ||||||||
\(681\) | 2.98683e8 | 0.945733 | ||||||||
\(682\) | 1.25772e9i | 3.96487i | ||||||||
\(683\) | 1.98182e8 | 0.622016 | 0.311008 | − | 0.950407i | \(-0.399333\pi\) | ||||
0.311008 | + | 0.950407i | \(0.399333\pi\) | |||||||
\(684\) | 5.31587e7i | 0.166114i | ||||||||
\(685\) | −5.27608e8 | −1.64149 | ||||||||
\(686\) | −357914. | −0.00110868 | ||||||||
\(687\) | 2.67331e8i | 0.824479i | ||||||||
\(688\) | −2.39033e8 | − | 1.49034e8i | −0.733995 | − | 0.457635i | ||||
\(689\) | 1.84617e8 | 0.564435 | ||||||||
\(690\) | 3.03001e8i | 0.922352i | ||||||||
\(691\) | − | 1.03318e8i | − | 0.313144i | −0.987667 | − | 0.156572i | \(-0.949956\pi\) | ||
0.987667 | − | 0.156572i | \(-0.0500443\pi\) | |||||||
\(692\) | −1.25411e9 | −3.78457 | ||||||||
\(693\) | 5.46521e8i | 1.64213i | ||||||||
\(694\) | −1.21194e8 | −0.362578 | ||||||||
\(695\) | − | 1.02801e8i | − | 0.306228i | ||||||
\(696\) | − | 4.89171e8i | − | 1.45089i | ||||||
\(697\) | −5.03158e7 | −0.148596 | ||||||||
\(698\) | −4.24328e8 | −1.24777 | ||||||||
\(699\) | 2.97006e8 | 0.869627 | ||||||||
\(700\) | − | 7.97905e6i | − | 0.0232625i | ||||||
\(701\) | 5.94012e8 | 1.72441 | 0.862207 | − | 0.506556i | \(-0.169082\pi\) | ||||
0.862207 | + | 0.506556i | \(0.169082\pi\) | |||||||
\(702\) | 6.24114e8 | 1.80407 | ||||||||
\(703\) | 5.63062e7 | 0.162065 | ||||||||
\(704\) | −6.49596e8 | −1.86177 | ||||||||
\(705\) | 1.79499e8 | 0.512266 | ||||||||
\(706\) | 1.82729e8i | 0.519270i | ||||||||
\(707\) | − | 3.23788e8i | − | 0.916226i | ||||||
\(708\) | 2.93938e8i | 0.828240i | ||||||||
\(709\) | −7.07249e7 | −0.198442 | −0.0992210 | − | 0.995065i | \(-0.531635\pi\) | ||||
−0.0992210 | + | 0.995065i | \(0.531635\pi\) | |||||||
\(710\) | − | 7.78429e8i | − | 2.17492i | ||||||
\(711\) | 1.36579e6 | 0.00379993 | ||||||||
\(712\) | 5.71888e8 | 1.58442 | ||||||||
\(713\) | −4.97929e8 | −1.37372 | ||||||||
\(714\) | − | 3.15079e8i | − | 0.865614i | ||||||
\(715\) | − | 6.85365e8i | − | 1.87501i | ||||||
\(716\) | 4.28335e8i | 1.16693i | ||||||||
\(717\) | − | 9.36875e7i | − | 0.254170i | ||||||
\(718\) | − | 2.67816e8i | − | 0.723542i | ||||||
\(719\) | 3.82388e7 | 0.102877 | 0.0514385 | − | 0.998676i | \(-0.483619\pi\) | ||||
0.0514385 | + | 0.998676i | \(0.483619\pi\) | |||||||
\(720\) | − | 2.28231e8i | − | 0.611474i | ||||||
\(721\) | − | 4.59177e8i | − | 1.22511i | ||||||
\(722\) | 6.37471e8i | 1.69375i | ||||||||
\(723\) | 9.36129e7 | 0.247697 | ||||||||
\(724\) | −7.89486e8 | −2.08031 | ||||||||
\(725\) | 5.21403e6i | 0.0136823i | ||||||||
\(726\) | −6.15517e8 | −1.60853 | ||||||||
\(727\) | − | 6.69439e8i | − | 1.74224i | −0.491071 | − | 0.871119i | \(-0.663395\pi\) | ||
0.491071 | − | 0.871119i | \(-0.336605\pi\) | |||||||
\(728\) | 1.01336e9 | 2.62646 | ||||||||
\(729\) | −1.41000e8 | −0.363946 | ||||||||
\(730\) | − | 1.77292e8i | − | 0.455743i | ||||||
\(731\) | 2.16925e8 | + | 1.35249e8i | 0.555338 | + | 0.346245i | ||||
\(732\) | 8.35552e7 | 0.213030 | ||||||||
\(733\) | − | 1.78625e8i | − | 0.453555i | −0.973947 | − | 0.226778i | \(-0.927181\pi\) | ||
0.973947 | − | 0.226778i | \(-0.0728191\pi\) | |||||||
\(734\) | 9.28538e8i | 2.34807i | ||||||||
\(735\) | −2.17043e8 | −0.546618 | ||||||||
\(736\) | − | 6.01174e7i | − | 0.150788i | ||||||
\(737\) | −1.29996e8 | −0.324734 | ||||||||
\(738\) | 1.10431e8i | 0.274740i | ||||||||
\(739\) | 6.78462e8i | 1.68109i | 0.541739 | + | 0.840547i | \(0.317766\pi\) | ||||
−0.541739 | + | 0.840547i | \(0.682234\pi\) | |||||||
\(740\) | −1.06742e9 | −2.63414 | ||||||||
\(741\) | −3.02607e7 | −0.0743744 | ||||||||
\(742\) | −4.95131e8 | −1.21202 | ||||||||
\(743\) | 2.72990e7i | 0.0665550i | 0.999446 | + | 0.0332775i | \(0.0105945\pi\) | ||||
−0.999446 | + | 0.0332775i | \(0.989405\pi\) | |||||||
\(744\) | −5.14055e8 | −1.24822 | ||||||||
\(745\) | 3.70988e8 | 0.897204 | ||||||||
\(746\) | 1.22456e9 | 2.94960 | ||||||||
\(747\) | −3.37487e8 | −0.809646 | ||||||||
\(748\) | −8.82772e8 | −2.10933 | ||||||||
\(749\) | 9.01287e8i | 2.14495i | ||||||||
\(750\) | 3.92850e8i | 0.931199i | ||||||||
\(751\) | 6.37092e8i | 1.50412i | 0.659095 | + | 0.752060i | \(0.270940\pi\) | ||||
−0.659095 | + | 0.752060i | \(0.729060\pi\) | |||||||
\(752\) | 3.44878e8 | 0.810984 | ||||||||
\(753\) | − | 3.94801e8i | − | 0.924683i | ||||||
\(754\) | −1.35611e9 | −3.16360 | ||||||||
\(755\) | 7.99875e8 | 1.85858 | ||||||||
\(756\) | −1.10726e9 | −2.56261 | ||||||||
\(757\) | 1.20716e8i | 0.278277i | 0.990273 | + | 0.139139i | \(0.0444334\pi\) | ||||
−0.990273 | + | 0.139139i | \(0.955567\pi\) | |||||||
\(758\) | − | 1.45116e9i | − | 3.33202i | ||||||
\(759\) | − | 3.85356e8i | − | 0.881328i | ||||||
\(760\) | 8.73033e7i | 0.198879i | ||||||||
\(761\) | − | 4.57356e8i | − | 1.03777i | −0.854844 | − | 0.518885i | \(-0.826347\pi\) | ||
0.854844 | − | 0.518885i | \(-0.173653\pi\) | |||||||
\(762\) | 3.90164e8 | 0.881824 | ||||||||
\(763\) | 4.52773e8i | 1.01931i | ||||||||
\(764\) | − | 1.03872e9i | − | 2.32927i | ||||||
\(765\) | 2.07122e8i | 0.462639i | ||||||||
\(766\) | 1.41679e9 | 3.15224 | ||||||||
\(767\) | 3.97908e8 | 0.881854 | ||||||||
\(768\) | − | 4.78687e8i | − | 1.05674i | ||||||
\(769\) | −3.76239e8 | −0.827341 | −0.413671 | − | 0.910427i | \(-0.635754\pi\) | ||||
−0.413671 | + | 0.910427i | \(0.635754\pi\) | |||||||
\(770\) | 1.83811e9i | 4.02623i | ||||||||
\(771\) | −1.02121e8 | −0.222819 | ||||||||
\(772\) | 6.04232e8 | 1.31326 | ||||||||
\(773\) | − | 6.60610e8i | − | 1.43023i | −0.699006 | − | 0.715116i | \(-0.746374\pi\) | ||
0.699006 | − | 0.715116i | \(-0.253626\pi\) | |||||||
\(774\) | 2.96840e8 | − | 4.76097e8i | 0.640175 | − | 1.02677i | ||||
\(775\) | 5.47927e6 | 0.0117711 | ||||||||
\(776\) | − | 1.05529e9i | − | 2.25832i | ||||||
\(777\) | 4.84533e8i | 1.03290i | ||||||||
\(778\) | 2.15923e8 | 0.458522 | ||||||||
\(779\) | − | 1.29602e7i | − | 0.0274158i | ||||||
\(780\) | 5.73663e8 | 1.20885 | ||||||||
\(781\) | 9.90005e8i | 2.07819i | ||||||||
\(782\) | − | 5.28321e8i | − | 1.10478i | ||||||
\(783\) | 7.23555e8 | 1.50725 | ||||||||
\(784\) | −4.17012e8 | −0.865368 | ||||||||
\(785\) | −5.18253e7 | −0.107135 | ||||||||
\(786\) | 7.14336e8i | 1.47108i | ||||||||
\(787\) | 2.37201e8 | 0.486622 | 0.243311 | − | 0.969948i | \(-0.421766\pi\) | ||||
0.243311 | + | 0.969948i | \(0.421766\pi\) | |||||||
\(788\) | 8.10737e8 | 1.65692 | ||||||||
\(789\) | 8.58293e7 | 0.174745 | ||||||||
\(790\) | 4.59355e6 | 0.00931680 | ||||||||
\(791\) | −2.99977e8 | −0.606121 | ||||||||
\(792\) | 9.46080e8i | 1.90437i | ||||||||
\(793\) | − | 1.13110e8i | − | 0.226820i | ||||||
\(794\) | − | 1.08673e9i | − | 2.17100i | ||||||
\(795\) | −1.36869e8 | −0.272397 | ||||||||
\(796\) | − | 2.25240e8i | − | 0.446586i | ||||||
\(797\) | −1.00665e8 | −0.198841 | −0.0994204 | − | 0.995046i | \(-0.531699\pi\) | ||||
−0.0994204 | + | 0.995046i | \(0.531699\pi\) | |||||||
\(798\) | 8.11572e7 | 0.159705 | ||||||||
\(799\) | −3.12980e8 | −0.613587 | ||||||||
\(800\) | 661539.i | 0.00129207i | ||||||||
\(801\) | 3.49474e8i | 0.680013i | ||||||||
\(802\) | − | 6.11117e8i | − | 1.18468i | ||||||
\(803\) | 2.25479e8i | 0.435472i | ||||||||
\(804\) | − | 1.08809e8i | − | 0.209361i | ||||||
\(805\) | −7.27706e8 | −1.39498 | ||||||||
\(806\) | 1.42510e9i | 2.72169i | ||||||||
\(807\) | 4.62936e7i | 0.0880847i | ||||||||
\(808\) | − | 5.60508e8i | − | 1.06255i | ||||||
\(809\) | 9.00670e8 | 1.70106 | 0.850531 | − | 0.525924i | \(-0.176281\pi\) | ||||
0.850531 | + | 0.525924i | \(0.176281\pi\) | |||||||
\(810\) | 1.83042e8 | 0.344426 | ||||||||
\(811\) | − | 9.34375e8i | − | 1.75170i | −0.482588 | − | 0.875848i | \(-0.660303\pi\) | ||
0.482588 | − | 0.875848i | \(-0.339697\pi\) | |||||||
\(812\) | 2.40591e9 | 4.49378 | ||||||||
\(813\) | − | 2.93358e8i | − | 0.545916i | ||||||
\(814\) | 2.05219e9 | 3.80490 | ||||||||
\(815\) | −3.92775e8 | −0.725556 | ||||||||
\(816\) | − | 1.67342e8i | − | 0.307989i | ||||||
\(817\) | −3.48372e7 | + | 5.58750e7i | −0.0638818 | + | 0.102459i | ||||
\(818\) | −9.95446e8 | −1.81869 | ||||||||
\(819\) | 6.19254e8i | 1.12724i | ||||||||
\(820\) | 2.45692e8i | 0.445605i | ||||||||
\(821\) | 3.91288e8 | 0.707077 | 0.353538 | − | 0.935420i | \(-0.384978\pi\) | ||||
0.353538 | + | 0.935420i | \(0.384978\pi\) | |||||||
\(822\) | 8.49040e8i | 1.52867i | ||||||||
\(823\) | 6.42442e8 | 1.15248 | 0.576241 | − | 0.817280i | \(-0.304519\pi\) | ||||
0.576241 | + | 0.817280i | \(0.304519\pi\) | |||||||
\(824\) | − | 7.94879e8i | − | 1.42076i | ||||||
\(825\) | 4.24050e6i | 0.00755189i | ||||||||
\(826\) | −1.06716e9 | −1.89361 | ||||||||
\(827\) | −1.54616e8 | −0.273361 | −0.136681 | − | 0.990615i | \(-0.543643\pi\) | ||||
−0.136681 | + | 0.990615i | \(0.543643\pi\) | |||||||
\(828\) | −7.67044e8 | −1.35123 | ||||||||
\(829\) | 9.58016e8i | 1.68155i | 0.541387 | + | 0.840774i | \(0.317899\pi\) | ||||
−0.541387 | + | 0.840774i | \(0.682101\pi\) | |||||||
\(830\) | −1.13507e9 | −1.98512 | ||||||||
\(831\) | 4.18114e8 | 0.728605 | ||||||||
\(832\) | −7.36046e8 | −1.27801 | ||||||||
\(833\) | 3.78442e8 | 0.654733 | ||||||||
\(834\) | −1.65431e8 | −0.285179 | ||||||||
\(835\) | 3.27660e8i | 0.562812i | ||||||||
\(836\) | − | 2.27382e8i | − | 0.389169i | ||||||
\(837\) | − | 7.60362e8i | − | 1.29671i | ||||||
\(838\) | 2.93571e8 | 0.498862 | ||||||||
\(839\) | 5.75769e8i | 0.974905i | 0.873149 | + | 0.487453i | \(0.162074\pi\) | ||||
−0.873149 | + | 0.487453i | \(0.837926\pi\) | |||||||
\(840\) | −7.51273e8 | −1.26754 | ||||||||
\(841\) | −9.77360e8 | −1.64311 | ||||||||
\(842\) | 1.04453e9 | 1.74979 | ||||||||
\(843\) | 1.40140e8i | 0.233926i | ||||||||
\(844\) | − | 1.17827e9i | − | 1.95982i | ||||||
\(845\) | − | 1.70691e8i | − | 0.282904i | ||||||
\(846\) | 6.86915e8i | 1.13447i | ||||||||
\(847\) | − | 1.47826e9i | − | 2.43277i | ||||||
\(848\) | −2.62971e8 | −0.431241 | ||||||||
\(849\) | 1.88516e8i | 0.308053i | ||||||||
\(850\) | 5.81370e6i | 0.00946664i | ||||||||
\(851\) | 8.12460e8i | 1.31830i | ||||||||
\(852\) | −8.28652e8 | −1.33984 | ||||||||
\(853\) | −8.03479e8 | −1.29458 | −0.647288 | − | 0.762245i | \(-0.724097\pi\) | ||||
−0.647288 | + | 0.762245i | \(0.724097\pi\) | |||||||
\(854\) | 3.03353e8i | 0.487052i | ||||||||
\(855\) | −5.33500e7 | −0.0853564 | ||||||||
\(856\) | 1.56021e9i | 2.48750i | ||||||||
\(857\) | −7.38940e8 | −1.17400 | −0.586998 | − | 0.809589i | \(-0.699690\pi\) | ||||
−0.586998 | + | 0.809589i | \(0.699690\pi\) | |||||||
\(858\) | −1.10291e9 | −1.74613 | ||||||||
\(859\) | 5.13638e8i | 0.810360i | 0.914237 | + | 0.405180i | \(0.132791\pi\) | ||||
−0.914237 | + | 0.405180i | \(0.867209\pi\) | |||||||
\(860\) | 6.60423e8 | − | 1.05924e9i | 1.03831 | − | 1.66533i | ||||
\(861\) | 1.11527e8 | 0.174731 | ||||||||
\(862\) | − | 2.76705e8i | − | 0.432012i | ||||||
\(863\) | 2.00925e8i | 0.312609i | 0.987709 | + | 0.156305i | \(0.0499582\pi\) | ||||
−0.987709 | + | 0.156305i | \(0.950042\pi\) | |||||||
\(864\) | 9.18022e7 | 0.142335 | ||||||||
\(865\) | − | 1.25862e9i | − | 1.94467i | ||||||
\(866\) | −3.14498e8 | −0.484244 | ||||||||
\(867\) | − | 2.02723e8i | − | 0.311061i | ||||||
\(868\) | − | 2.52830e9i | − | 3.86607i | ||||||
\(869\) | −5.84207e6 | −0.00890240 | ||||||||
\(870\) | 1.00538e9 | 1.52676 | ||||||||
\(871\) | −1.47296e8 | −0.222914 | ||||||||
\(872\) | 7.83793e8i | 1.18209i | ||||||||
\(873\) | 6.44874e8 | 0.969243 | ||||||||
\(874\) | 1.36084e8 | 0.203832 | ||||||||
\(875\) | −9.43492e8 | −1.40836 | ||||||||
\(876\) | −1.88730e8 | −0.280756 | ||||||||
\(877\) | 1.01198e9 | 1.50029 | 0.750143 | − | 0.661276i | \(-0.229985\pi\) | ||||
0.750143 | + | 0.661276i | \(0.229985\pi\) | |||||||
\(878\) | − | 1.54890e9i | − | 2.28844i | ||||||
\(879\) | 5.88400e8i | 0.866375i | ||||||||
\(880\) | 9.76243e8i | 1.43255i | ||||||||
\(881\) | 5.05542e8 | 0.739315 | 0.369657 | − | 0.929168i | \(-0.379475\pi\) | ||||
0.369657 | + | 0.929168i | \(0.379475\pi\) | |||||||
\(882\) | − | 8.30589e8i | − | 1.21054i | ||||||
\(883\) | −1.59838e8 | −0.232165 | −0.116083 | − | 0.993240i | \(-0.537034\pi\) | ||||
−0.116083 | + | 0.993240i | \(0.537034\pi\) | |||||||
\(884\) | −1.00025e9 | −1.44795 | ||||||||
\(885\) | −2.94996e8 | −0.425585 | ||||||||
\(886\) | − | 1.37717e9i | − | 1.98009i | ||||||
\(887\) | − | 9.41893e7i | − | 0.134968i | −0.997720 | − | 0.0674840i | \(-0.978503\pi\) | ||
0.997720 | − | 0.0674840i | \(-0.0214972\pi\) | |||||||
\(888\) | 8.38772e8i | 1.19786i | ||||||||
\(889\) | 9.37041e8i | 1.33369i | ||||||||
\(890\) | 1.17538e9i | 1.66728i | ||||||||
\(891\) | −2.32793e8 | −0.329107 | ||||||||
\(892\) | − | 6.84138e8i | − | 0.963938i | ||||||
\(893\) | − | 8.06167e7i | − | 0.113206i | ||||||
\(894\) | − | 5.97004e8i | − | 0.835535i | ||||||
\(895\) | −4.29877e8 | −0.599618 | ||||||||
\(896\) | 1.81783e9 | 2.52714 | ||||||||
\(897\) | − | 4.36641e8i | − | 0.604988i | ||||||
\(898\) | 3.08528e8 | 0.426054 | ||||||||
\(899\) | 1.65216e9i | 2.27391i | ||||||||
\(900\) | 8.44064e6 | 0.0115784 | ||||||||
\(901\) | 2.38648e8 | 0.326275 | ||||||||
\(902\) | − | 4.72360e8i | − | 0.643656i | ||||||
\(903\) | −4.80822e8 | − | 2.99785e8i | −0.653012 | − | 0.407143i | ||||
\(904\) | −5.19289e8 | −0.702917 | ||||||||
\(905\) | − | 7.92326e8i | − | 1.06895i | ||||||
\(906\) | − | 1.28718e9i | − | 1.73083i | ||||||
\(907\) | −6.00542e8 | −0.804863 | −0.402431 | − | 0.915450i | \(-0.631835\pi\) | ||||
−0.402431 | + | 0.915450i | \(0.631835\pi\) | |||||||
\(908\) | 2.54302e9i | 3.39698i | ||||||||
\(909\) | 3.42519e8 | 0.456030 | ||||||||
\(910\) | 2.08273e9i | 2.76381i | ||||||||
\(911\) | − | 6.16272e8i | − | 0.815112i | −0.913180 | − | 0.407556i | \(-0.866381\pi\) | ||
0.913180 | − | 0.407556i | \(-0.133619\pi\) | |||||||
\(912\) | 4.31037e7 | 0.0568237 | ||||||||
\(913\) | 1.44357e9 | 1.89682 | ||||||||
\(914\) | 3.74900e8 | 0.490995 | ||||||||
\(915\) | 8.38558e7i | 0.109464i | ||||||||
\(916\) | −2.27609e9 | −2.96144 | ||||||||
\(917\) | −1.71559e9 | −2.22488 | ||||||||
\(918\) | 8.06771e8 | 1.04285 | ||||||||
\(919\) | −8.93789e8 | −1.15156 | −0.575782 | − | 0.817603i | \(-0.695302\pi\) | ||||
−0.575782 | + | 0.817603i | \(0.695302\pi\) | |||||||
\(920\) | −1.25973e9 | −1.61776 | ||||||||
\(921\) | 4.32689e8i | 0.553856i | ||||||||
\(922\) | 1.52484e9i | 1.94550i | ||||||||
\(923\) | 1.12176e9i | 1.42657i | ||||||||
\(924\) | 1.95670e9 | 2.48032 | ||||||||
\(925\) | − | 8.94040e6i | − | 0.0112962i | ||||||
\(926\) | 6.05651e7 | 0.0762763 | ||||||||
\(927\) | 4.85741e8 | 0.609769 | ||||||||
\(928\) | −1.99473e8 | −0.249598 | ||||||||
\(929\) | − | 2.69100e8i | − | 0.335634i | −0.985818 | − | 0.167817i | \(-0.946328\pi\) | ||
0.985818 | − | 0.167817i | \(-0.0536718\pi\) | |||||||
\(930\) | − | 1.05652e9i | − | 1.31349i | ||||||
\(931\) | 9.74783e7i | 0.120798i | ||||||||
\(932\) | 2.52874e9i | 3.12361i | ||||||||
\(933\) | 3.40321e8i | 0.419029i | ||||||||
\(934\) | −2.18515e8 | −0.268189 | ||||||||
\(935\) | − | 8.85948e8i | − | 1.08386i | ||||||
\(936\) | 1.07199e9i | 1.30726i | ||||||||
\(937\) | − | 7.80873e8i | − | 0.949209i | −0.880199 | − | 0.474604i | \(-0.842591\pi\) | ||
0.880199 | − | 0.474604i | \(-0.157409\pi\) | |||||||
\(938\) | 3.95039e8 | 0.478665 | ||||||||
\(939\) | 2.88975e8 | 0.349031 | ||||||||
\(940\) | 1.52828e9i | 1.84001i | ||||||||
\(941\) | 7.33080e8 | 0.879797 | 0.439899 | − | 0.898047i | \(-0.355014\pi\) | ||||
0.439899 | + | 0.898047i | \(0.355014\pi\) | |||||||
\(942\) | 8.33987e7i | 0.0997715i | ||||||||
\(943\) | 1.87007e8 | 0.223010 | ||||||||
\(944\) | −5.66785e8 | −0.673756 | ||||||||
\(945\) | − | 1.11124e9i | − | 1.31678i | ||||||
\(946\) | −1.26971e9 | + | 2.03647e9i | −1.49979 | + | 2.40550i | ||||
\(947\) | −2.44558e8 | −0.287960 | −0.143980 | − | 0.989581i | \(-0.545990\pi\) | ||||
−0.143980 | + | 0.989581i | \(0.545990\pi\) | |||||||
\(948\) | − | 4.88992e6i | − | 0.00573953i | ||||||
\(949\) | 2.55487e8i | 0.298930i | ||||||||
\(950\) | −1.49748e6 | −0.00174659 | ||||||||
\(951\) | − | 2.76571e8i | − | 0.321562i | ||||||
\(952\) | 1.30994e9 | 1.51824 | ||||||||
\(953\) | − | 4.37161e8i | − | 0.505083i | −0.967586 | − | 0.252542i | \(-0.918734\pi\) | ||
0.967586 | − | 0.252542i | \(-0.0812665\pi\) | |||||||
\(954\) | − | 5.23775e8i | − | 0.603253i | ||||||
\(955\) | 1.04246e9 | 1.19688 | ||||||||
\(956\) | 7.97668e8 | 0.912953 | ||||||||
\(957\) | −1.27864e9 | −1.45885 | ||||||||
\(958\) | − | 7.78709e8i | − | 0.885684i | ||||||
\(959\) | −2.03911e9 | −2.31198 | ||||||||
\(960\) | 5.45680e8 | 0.616772 | ||||||||
\(961\) | 8.48698e8 | 0.956276 | ||||||||
\(962\) | 2.32530e9 | 2.61188 | ||||||||
\(963\) | −9.53427e8 | −1.06760 | ||||||||
\(964\) | 7.97032e8i | 0.889702i | ||||||||
\(965\) | 6.06406e8i | 0.674810i | ||||||||
\(966\) | 1.17104e9i | 1.29910i | ||||||||
\(967\) | −9.59605e8 | −1.06124 | −0.530620 | − | 0.847610i | \(-0.678041\pi\) | ||||
−0.530620 | + | 0.847610i | \(0.678041\pi\) | |||||||
\(968\) | − | 2.55901e9i | − | 2.82128i | ||||||
\(969\) | −3.91169e7 | −0.0429926 | ||||||||
\(970\) | 2.16890e9 | 2.37642 | ||||||||
\(971\) | 1.64448e9 | 1.79627 | 0.898135 | − | 0.439721i | \(-0.144923\pi\) | ||||
0.898135 | + | 0.439721i | \(0.144923\pi\) | |||||||
\(972\) | − | 1.85872e9i | − | 2.02402i | ||||||
\(973\) | − | 3.97308e8i | − | 0.431310i | ||||||
\(974\) | − | 1.13579e9i | − | 1.22920i | ||||||
\(975\) | 4.80484e6i | 0.00518400i | ||||||||
\(976\) | 1.61115e8i | 0.173295i | ||||||||
\(977\) | −6.22718e8 | −0.667741 | −0.333870 | − | 0.942619i | \(-0.608355\pi\) | ||||
−0.333870 | + | 0.942619i | \(0.608355\pi\) | |||||||
\(978\) | 6.32064e8i | 0.675685i | ||||||||
\(979\) | − | 1.49485e9i | − | 1.59312i | ||||||
\(980\) | − | 1.84793e9i | − | 1.96340i | ||||||
\(981\) | −4.78966e8 | −0.507338 | ||||||||
\(982\) | 1.44356e9 | 1.52441 | ||||||||
\(983\) | − | 1.74231e9i | − | 1.83428i | −0.398568 | − | 0.917139i | \(-0.630493\pi\) | ||
0.398568 | − | 0.917139i | \(-0.369507\pi\) | |||||||
\(984\) | 1.93064e8 | 0.202635 | ||||||||
\(985\) | 8.13654e8i | 0.851395i | ||||||||
\(986\) | −1.75300e9 | −1.82874 | ||||||||
\(987\) | 6.93732e8 | 0.721507 | ||||||||
\(988\) | − | 2.57643e8i | − | 0.267145i | ||||||
\(989\) | −8.06238e8 | − | 5.02677e8i | −0.833440 | − | 0.519638i | ||||
\(990\) | −1.94444e9 | −2.00396 | ||||||||
\(991\) | 1.80104e8i | 0.185056i | 0.995710 | + | 0.0925280i | \(0.0294948\pi\) | ||||
−0.995710 | + | 0.0925280i | \(0.970505\pi\) | |||||||
\(992\) | 2.09620e8i | 0.214733i | ||||||||
\(993\) | −3.14729e8 | −0.321432 | ||||||||
\(994\) | − | 3.00848e9i | − | 3.06329i | ||||||
\(995\) | 2.26050e8 | 0.229475 | ||||||||
\(996\) | 1.20830e9i | 1.22291i | ||||||||
\(997\) | 1.33198e9i | 1.34404i | 0.740534 | + | 0.672019i | \(0.234573\pi\) | ||||
−0.740534 | + | 0.672019i | \(0.765427\pi\) | |||||||
\(998\) | −1.29599e9 | −1.30380 | ||||||||
\(999\) | −1.24067e9 | −1.24439 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 43.7.b.b.42.19 | yes | 20 | |
43.42 | odd | 2 | inner | 43.7.b.b.42.2 | ✓ | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
43.7.b.b.42.2 | ✓ | 20 | 43.42 | odd | 2 | inner | |
43.7.b.b.42.19 | yes | 20 | 1.1 | even | 1 | trivial |